Starting from the Maxwell–Boltzmann distribution, eq. (18.10)

for the probability of finding a particle with energy E in a gas with temperature T, show that the most probable speed for a particle is v̅ = √2k_BT/m, but that the average speed of a particle is 〈v〉 = √8k_BT/πm. Verify that the most probable speed for a neutron at T = 20^◦C is ∼2200m/s.

Transcribed Image Text:

dPB VEe-E/kBT (7 kB T)3/2 dE